Year: 2025
Type: article
Abstract: We investigate the “natural” locus of definition of Abel-Jacobi maps. In particular, we show that, for a proper, geometrically reduced curve C – not necessarily smooth – the Abel-Jacobi map from the smooth locus $$C^{\textrm{sm}}$$ C sm into the Jacobian of C does not extend to any larger (separated, geometrically reduced) curve containing $$C^{\textrm{sm}}$$ C sm except under certain particular circumstances which we describe explicitly. As a consequence, we deduce that the Abel-Jacobi map has closed image except in certain explicitly described circumstances, and that it is always a closed embedding for irreducible curves not isomorphic to $$\textbf{P}^1$$ P 1 .
Author: Zev Rosengarten
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funder: Hebrew University of Jerusalem
OpenAlex ID: W7117365073